Question

1) (14y+21)(1.8-0.3y)=0 2) 2(4x+1)-x=7x+3

Answer 1

1.
(14y + 21) = 0, или  (1.8 - 0.3y) = 0
1) 14y + 21 = 0
    14y = -21
    y = -1.5
2) 1.8 - 0.3y = 0
    18 - 3y = 0
    -3y = -18
    y = 6
Ответ: y1 = -1.5;
y2 = 6.

2.
2(4x - 1) - x = 7x + 3;
8x + 2 - x = 7x + 3;
8x - x - 7x = 3 - 2;
0 ≠ 1 = > (корней нет).

Answer 2

Let's solve each equation step by step:

1. (14y + 21)(1.8 - 0.3y) = 0

To solve this equation, we can use the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero.

So, we set each factor to zero and solve for 'y':

Setting the first factor to zero: 14y + 21 = 0 Subtract 21 from both sides: 14y = -21 Divide by 14: y = -21/14 y = -3/2

Setting the second factor to zero: 1.8 - 0.3y = 0 Subtract 1.8 from both sides: -0.3y = -1.8 Divide by -0.3: y = (-1.8) / (-0.3) y = 6

So the solutions to the equation are y = -3/2 and y = 6.

2. 2(4x + 1) - x = 7x + 3

Let's simplify and solve for 'x':

Distribute the 2 on the left side: 8x + 2 - x = 7x + 3

Combine like terms: 7x + 2 = 7x + 3

Now, we can see that the variable 'x' is canceled out from both sides of the equation. This implies that there is no unique solution for 'x', and the equation is inconsistent. In other words, there is no value of 'x' that satisfies the equation.

The reason for this inconsistency is that the equation results in a statement that contradicts itself, indicating that there are no valid solutions for 'x' that would make the equation true.